Properties such as boiling point, freezing point, and vapour pressure of a pure solvent change when solute molecules are added to get homogenous solution. These are called colligative properties.
Anwer the following questions:
i.0.1 M ethanol
ii.`0.1 m Ba_(3)(PO_(4))_(3)`
iii.`0.1 m Na_(2)SO_(4)`
Increasing order of freezing points

Options

A. `(ii) lt (iii) lt (i)`
B. `(iii) lt (ii) lt (i)`
C. `(i) lt (ii) lt (iii)`
D. `(ii) lt (i) lt (iii)`

Explanation

To solve the problem regarding the freezing points of the given solutions, we will follow these steps:

### Step 1: Understand Colligative Properties
Colligative properties depend on the number of solute particles in a solution, not on the identity of the solute. The freezing point depression (ΔTf) is given by the formula:
\[ \Delta T_f = i \cdot K_f \cdot m \]
where:
- \( i \) = van 't Hoff factor (number of particles the solute dissociates into)
- \( K_f \) = freezing point depression constant (depends on the solvent)
- \( m \) = molality of the solution

### Step 2: Calculate for 0.1 M Ethanol (C2H5OH)
Ethanol is a non-electrolyte, meaning it does not dissociate into ions. Therefore:
- \( i = 1 \)
- \( m = 0.1 \)

Using the formula:
\[ \Delta T_f = 1 \cdot K_f \cdot 0.1 \]
This gives us a value of \( \Delta T_f = 0.1 K_f \).

### Step 3: Calculate for 0.1 m Ba3(PO4)2
Barium phosphate dissociates into 5 ions:
\[ Ba_3(PO_4)_2 \rightarrow 3Ba^{2+} + 2PO_4^{3-} \]
Thus:
- \( i = 5 \)
- \( m = 0.1 \)

Using the formula:
\[ \Delta T_f = 5 \cdot K_f \cdot 0.1 \]
This gives us a value of \( \Delta T_f = 0.5 K_f \).

### Step 4: Calculate for 0.1 m Na2SO4
Sodium sulfate dissociates into 3 ions:
\[ Na_2SO_4 \rightarrow 2Na^{+} + SO_4^{2-} \]
Thus:
- \( i = 3 \)
- \( m = 0.1 \)

Using the formula:
\[ \Delta T_f = 3 \cdot K_f \cdot 0.1 \]
This gives us a value of \( \Delta T_f = 0.3 K_f \).

### Step 5: Compare the ΔTf Values
Now we have:
1. Ethanol: \( \Delta T_f = 0.1 K_f \)
2. Barium phosphate: \( \Delta T_f = 0.5 K_f \)
3. Sodium sulfate: \( \Delta T_f = 0.3 K_f \)

### Step 6: Determine Freezing Points
Since the freezing point decreases with an increase in \( \Delta T_f \):
- The solution with the highest \( \Delta T_f \) (0.1 K_f) will have the highest freezing point (ethanol).
- The solution with the next highest \( \Delta T_f \) (0.3 K_f) will have a lower freezing point (sodium sulfate).
- The solution with the highest \( \Delta T_f \) (0.5 K_f) will have the lowest freezing point (barium phosphate).

### Step 7: Write the Increasing Order of Freezing Points
Thus, the increasing order of freezing points is:
1. Barium phosphate (lowest freezing point)
2. Sodium sulfate
3. Ethanol (highest freezing point)

### Final Answer
The increasing order of freezing points is:
**Ba3(PO4)2 < Na2SO4 < C2H5OH**

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